Most building and household debris is fine. The limits here come from the city's own rules and from the recycling authority's lists rather than from a long state table.
Hazardous waste and industrial special waste are excluded from the city's definition of solid waste altogether, so they are out of any container by definition. In practice that means paint, solvents, fuel, pool chemicals, full aerosol cans, wet asphalt sealer, cooking oil and batteries go to a household hazardous waste collection rather than into your container.
The city also bars disposing of waste inside the city by burial or dumping, and bars using it as fill. On a Farmington Hills tear-out that matters: broken concrete and soil cannot simply be buried in a back corner of the lot, even on your own land.
Electronics, polystyrene foam and household hazardous material are refused at the authority's recycling drop-off, so none of those should be mixed into a container on the assumption that they can be sorted out later.
Asbestos belongs nowhere in a container. On a house or a commercial building from before the mid-1980s, pipe wrap, floor tile mastic and some textured ceilings are worth testing before demolition begins.
Yard waste has its own seasonal route in Farmington Hills, running roughly from early April to mid-December, so leaves, grass and brush should stay out of a construction container.
If an item is not clearly on one side of the line, ask your account manager before it is loaded. One refused item can stall a whole load.